Damage Identification and Quantification in Beams Using Wigner-Ville Distribution

Abstract

The paper presents the novel method of damage identification and quantification in beams using the Wigner-Ville distribution (WVD). The presented non-parametric method is characterized by high sensitivity to a local stiffness decrease due to the presence of damage, comparable with the sensitivity of the wavelet-based approaches, however the lack of selection of the parameters of the algorithm, like wavelet type and its order, and the possibility of reduction of the boundary effect make this method advantageous with respect to the mentioned wavelet-based approaches. Moreover, the direct relation between the energy density resulting from the application of WVD to modal rotations make it possible to quantify damage in terms of its width and depth. The results obtained for the numerical modal rotations of a beam presented in this paper, simulating the results of non-destructive testing achievable with the shearography non-destructive testing method, confirm high accuracy in localization of a damage as well as quantification of its dimensions. It was shown that the WVD-based method is suitable for detection of damage represented by the stiffness decrease of 1% and can be identified and quantified with a high precision. The presented results of quantification allowed extracting information on damage width and depth.

Time-frequency methods of non-stationary vibroacoustic diagnostic signals processing

“…For this reason, it can be defined as a bilinear transform. WVD is characterized by scaling and shift properties, like WT, which makes it useful in the context of numerical applications, including identification of faults using the analysed signals [16]. Taking into account the optimal resolution and the momentary spectrum of power density in time and frequency domains, WVD is considered as particularly useful in diagnosing the rotating machines [9,17,25,40].…”

“…Z tego powodu można ją określić jako transformatę biliniową. WVD charakteryzuje się własnościami skalowania i przesunięcia, podobnie jak WT, co czyni ją przydatną w kontekście zastosowań numerycznych, w tym identyfikacji uszkodzeń za pomocą analizowanych sygnałów [16]. Biorąc pod uwagę optymalną rozdzielczość i widmo chwilowe gęstości mocy w dziedzinach czasu i częstotliwości, WVD jest uznawana za szczególnie przydatną w diagnozowaniu maszyn wirujących [9,17,25,40].…”

Accelerated Editing Method for Vehicle Durability Fatigue Load Spectrum Based on Wigner-Ville Transform

“…The WV distribution analysis is widely used in structural non-stationary signal analysis, fault condition monitoring, damage detection, etc. [ 25 , 26 , 27 , 28 ] Levy et al [ 25 , 26 ] proposed a new WV distribution technique-based time-frequency metric for the characterization of frequency sources, which could be used to solve problems of amplitude fluctuations, phase noise, and frequency instabilities caused by the physical mechanisms of such as the oscillators, clocks, etc. Singru et al [ 27 ] examined an experimental method for condition monitoring of bearing failures by utilizing experimental vibration signatures.…”

“…It showed that the WV distribution analysis is more accurate and effective in both time and frequency domain numerical characterization of the obtained vibration signals than other methods, such as FFT. Andrzej [ 28 ] put forward a novel non-parametric damage identification algorithm based on the WV distribution, which exhibits high precision of localization and quantification in damage detection. It also revealed that the WV distribution analysis possesses the advantage that there is no need for parameter selection in the algorithm such as wavelet type and its order, as well as the possibility to reduce the boundary impact.…”

Assessment of Internal Damage in Sandwich Structures by Post-Processing of Mode Shapes Using Curvelet Transform

“…Another problem appearing during the application of WTs is the presence of the boundary effect, causing a significant increase of the resulting wavelet coefficients in the vicinity of borders of a tested structure. To overcome these deficiencies, some non-parametric methods were applied for damage identification, including cross-correlation [ 35 ], Vigner-Wille distribution [ 36 ], and S-transform [ 37 ]. However, a problem with properly filtering out the damage signatures from processed mode shapes or curvatures remains open in the area of structural damage identification.…”